Question

If sin(x) = 2/3, what is tan(2x)?

Answer 1

`4sqrt5`

Explanation:

`sin x = 2/3` , find cos x.
`cos^2 x = 1 - sin^2 x = 1 - 4/9 = 5/9`
`cos x = +- sqrt5/3`
Since x is in Quadrant I, then, cos x is positive
`cos x = sqrt5/3`
`tan x = sin x/(cos x) = (2/3)(3/sqrt5) = 2/sqrt5 = (2sqrt5)/5`
Apply the trig identity:
`tan 2x = (2tan x)/(1 - tan^2 x)`
`tan 2x = ((4sqrt5)/5)/(1 - 4/5) = (4sqrt5/5)(5/1) = 4sqrt5`